package com.freetymekiyan.algorithms.level.medium;

/**
 * 313. Super Ugly Number
 * <p>
 * Write a program to find the nth super ugly number.
 * <p>
 * Super ugly numbers are positive numbers whose all prime factors are in the given prime list primes of size k. For
 * example, [1, 2, 4, 7, 8, 13, 14, 16, 19, 26, 28, 32] is the sequence of the first 12 super ugly numbers given primes
 * = [2, 7, 13, 19] of size 4.
 * <p>
 * Note:
 * (1) 1 is a super ugly number for any given primes.
 * (2) The given numbers in primes are in ascending order.
 * (3) 0 < k ≤ 100, 0 < n ≤ 106, 0 < primes[i] < 1000.
 * <p>
 * Tags: Math, Heap
 * Similar Problems: (M) Ugly Number II
 */

public class SuperUglyNumber {

  /**
   * Refer to ugly number 2
   * Use an array to keep all indices for primes
   */
  public int nthSuperUglyNumber(int n, int[] primes) {
    int len = primes.length;
    int[] index = new int[len];
    int[] res = new int[n];
    res[0] = 1;
    for (int i = 1; i < n; i++) {
      int min = Integer.MAX_VALUE;
      for (int j = 0; j < len; j++) {
        min = Math.min(res[index[j]] * primes[j], min);
      }
      res[i] = min;
      for (int j = 0; j < len; j++) {
        if (res[i] % primes[j] == 0) index[j]++;
      }
    }
    return res[n - 1];
  }
}
